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Accepted · first revision · record

Title: Nonperturbative completion of the string genus expansion
Plain: String theory computes processes as a sum over surfaces with more and more holes, and the sum diverges like factorials. Which nonperturbative effects complete it, and whether the result is unique, is known only in toy models and special settings.
Precise: String perturbation theory in $g_{s}$ grows like $(2g)!$ at genus $g$ (Shenker 1990), which points to effects of order $\exp(-1/g_{s})$ from D-branes. For the type II superstring in $10\mathrm{D}$ flat space, determine whether the genus expansion of the four-graviton amplitude at fixed kinematics is resurgent, and whether D-instanton sectors give a unique median-resummed result.
Settled by: An exact transseries for the flat-space four-graviton amplitude, with D-instanton coefficients fixed and the resummed result matched to an independent nonperturbative computation.
Kind: well-posed
Answer type: yes-no
References: (empty)
Literature status: open
Status note: Resurgent transseries are known for minimal strings, JT-gravity matrix models and $N=4$ super-Yang-Mills integrated correlators (2021-2024); the flat-space critical superstring amplitude remains open.
Posed since: 1990